CHAPTER33WAVES.BREAKERSANDSUREOCEANWAVES3300.Introduction3302.WaveCharacteristicsOcean Waves arethemost widelyobservedphenome-Ocean waves are very nearly in the shape of an invert-non at sea,and possiblytheleast understood bytheaverageed cycloid, the figure formed by a point inside the rim ofaseaman.Morethananyothersinglefactor.oceanwavesarewheel rolling along a level surface.This shape is shown inlikely to cause a navigator to change course or speed toFigure3302a.Thehighestparts of waves arecalled crestsavoid damageto ship and cargo.Wind-generated oceanand the intervening lowest parts, troughs.Since the crestswaves have been measured at more than 100feet high, andare steeperand narrower than the troughs, the mean or stilltsunamis, caused by earthquakes, far higher.A marinerwater level is a little lower than halfwaybetween the crestswithknowledgeof basic facts concerning waves is abletoand troughs.The vertical distancebetween trough and crestusethem to hisadvantage,avoid hazardous conditions,andis called wave height, labeled H in Figure3302a.The hor-operatewithaminimumofdangerif suchconditionscan-izontal distancebetween successivecrests,measured inthenot be avoided. See Chapter 38, Weather Routing, fordirection of travel, is called wavelength, labeled L.Thedetails on howto avoid areas of severe waves.time interval between passage of successive crests ata sta-tionary point is called wave period (P). Wave height,3301.CausesOfWaveslength,andperiod depend upon anumberoffactors,suchas thewind speed,thelength oftime it has blown, and itsWaves on the surface ofthe sea are caused principallyfetch (the straight distance it has traveled over the surface)by wind, but other factors, such as submarine earthquakes,Table 3302 indicates the relationshipbetween wind speed.volcanic eruptions, and the tide, also cause waves.If afetch,lengthoftimethewindblows,waveheight,andwavebreezeof lessthan2knotsstartstoblowacrosssmoothwa-period in deep water.ter,smallwaveletscalledripplesformalmostinstantaneously.When the breeze dies, the ripples disap-pear as suddenly as they formed, the level surface beingrestored by surface tension of the water.If thewind speedexceeds2knots,more stablegravitywavesgraduallyform,and progress withthewind.While thegenerating wind blows, the resulting wavesmay be referred to as sea.When the wind stops or changesSTILLWATERLEVELdirection.wavesthatcontinueonwithoutrelationtolocalwinds are called swell.Unlike wind and current, waves are not deflected ap-Figure 3302a. A typical sea wave.preciably by the rotation of the earth, but move in thedirection in whichthegeneratingwindblows.WhenthisIf thewater is deeperthan one-half the wavelength (L)wind ceases,friction and spreading cause the waves to bethis length in feet is theoretically related to period (P) inreduced in height, or attenuated, as they move.However.seconds by the formula:the reduction takes place so slowly that swell often contin-uesuntilitreachessomeobstruction,suchasashoreL = 5.12 p2TheFleet Numerical Meteorology and OceanographyCenterproduces synopticanalysesandpredictionsofoceanThe actual value has been found to be a little less thanwave heights using a spectral numerical model.The wavethis for swell, and about two-thirds the length determinedinformationconsistsofheightsanddirectionsfordifferentby this formulafor sea.When the waves leave the generat-periods and wavelengths.Verification of projected data hasproventhemodeltobeverygood.Informationfromtheing area and continue as freewaves,the wavelength andmodel is provided to the U.S.Navy on a routine basis and isperiodcontinue to increase, whiletheheight decreases.Theavital inputtotheOptimumTrackShipRoutingprogram.rateofchangegraduallydecreases.443
443 CHAPTER 33 WAVES, BREAKERS AND SURF OCEAN WAVES 3300. Introduction Ocean Waves are the most widely observed phenomenon at sea, and possibly the least understood by the average seaman. More than any other single factor, ocean waves are likely to cause a navigator to change course or speed to avoid damage to ship and cargo. Wind-generated ocean waves have been measured at more than 100 feet high, and tsunamis, caused by earthquakes, far higher. A mariner with knowledge of basic facts concerning waves is able to use them to his advantage, avoid hazardous conditions, and operate with a minimum of danger if such conditions cannot be avoided. See Chapter 38, Weather Routing, for details on how to avoid areas of severe waves. 3301. Causes Of Waves Waves on the surface of the sea are caused principally by wind, but other factors, such as submarine earthquakes, volcanic eruptions, and the tide, also cause waves. If a breeze of less than 2 knots starts to blow across smooth water, small wavelets called ripples form almost instantaneously. When the breeze dies, the ripples disappear as suddenly as they formed, the level surface being restored by surface tension of the water. If the wind speed exceeds 2 knots, more stable gravity waves gradually form, and progress with the wind. While the generating wind blows, the resulting waves may be referred to as sea. When the wind stops or changes direction, waves that continue on without relation to local winds are called swell. Unlike wind and current, waves are not deflected appreciably by the rotation of the earth, but move in the direction in which the generating wind blows. When this wind ceases, friction and spreading cause the waves to be reduced in height, or attenuated, as they move. However, the reduction takes place so slowly that swell often continues until it reaches some obstruction, such as a shore. The Fleet Numerical Meteorology and Oceanography Center produces synoptic analyses and predictions of ocean wave heights using a spectral numerical model. The wave information consists of heights and directions for different periods and wavelengths. Verification of projected data has proven the model to be very good. Information from the model is provided to the U.S. Navy on a routine basis and is a vital input to the Optimum Track Ship Routing program. 3302. Wave Characteristics Ocean waves are very nearly in the shape of an inverted cycloid, the figure formed by a point inside the rim of a wheel rolling along a level surface. This shape is shown in Figure 3302a. The highest parts of waves are called crests, and the intervening lowest parts, troughs. Since the crests are steeper and narrower than the troughs, the mean or still water level is a little lower than halfway between the crests and troughs. The vertical distance between trough and crest is called wave height, labeled H in Figure 3302a. The horizontal distance between successive crests, measured in the direction of travel, is called wavelength, labeled L. The time interval between passage of successive crests at a stationary point is called wave period (P). Wave height, length, and period depend upon a number of factors, such as the wind speed, the length of time it has blown, and its fetch (the straight distance it has traveled over the surface). Table 3302 indicates the relationship between wind speed, fetch, length of time the wind blows, wave height, and wave period in deep water. If the water is deeper than one-half the wavelength (L), this length in feet is theoretically related to period (P) in seconds by the formula: The actual value has been found to be a little less than this for swell, and about two-thirds the length determined by this formula for sea. When the waves leave the generating area and continue as free waves, the wavelength and period continue to increase, while the height decreases. The rate of change gradually decreases. Figure 3302a. A typical sea wave. L 5.12 P2 =
Pa8.218.81313.015.011.034.01020.0415.20.511.9035.0e100851202.04. 2227.86..14.32127.7.933.3X.411.312012.39388806666125881800204.322235.514014036.625.8511917.616.2014.813.913.092040.07N星星房宾强43.28823nni19.160O1615.44150423259.44017. 095&18.06850.0215"10.0633.21.O232319Oo17.120041.546.R3634239.6222088008双332a欢欢欢验i2i2o17.N559.0488010E204845.4499.10.010.28.18.00082550Q525.53004544.312.729..007o.2010.28018.400*3a47.0213118.2500K2230048.07.230.22710.6区0玖观#板板板机3201333.0P09.6o11.18..5298.0319.8134013213.o034..60.0418.55124板888013.9635.90930.O110360218.6055.121328.37.18.a2510.0.3113800122842647a2.512.40010.28.38.N宇军多多家家目5强现4042026.R38V41033R83区区区55510烈强玖汉科44ini30.9星学0o6o618.990-45双儿卫.05019.5552610.1.849944.O012.19.8.213010495004512T3.84455050欢欢机机4310.19,61338.C013.825173455.010.41.19.n0ot酒洗544473019.142058..3602O08500BN区200056de15n95063.0550100052Table 3302. Minimum Time (T) in hours that wind must blow to form waves of H significant height (in feet) and P period (in secconds). Fetch in nautical miles
4 4 4 W A V E S , B R E A K E R S AN D S U R F BEAUFORT NUMBER Fetch Fetch 3 4 5 6 7 8 9 10 11 T H P T H P T H P T H P T H P T H P T H P T H P T H P 10 4. 4 1. 8 2. 1 3. 7 2. 6 2. 4 3. 2 3. 5 2. 8 2. 7 5. 0 3. 1 2. 5 6. 0 3. 4 2. 3 7. 3 3. 9 2. 0 8. 0 4. 1 1. 9 10. 0 4. 2 1. 8 10. 0 5. 0 10 20 7. 1 2. 0 2. 5 6. 2 3. 2 2. 9 5. 4 4. 9 3. 3 4. 7 7. 0 3. 8 4. 2 8. 6 4. 3 3. 9 10. 0 4. 4 3. 5 12. 0 5. 0 3. 2 14. 0 5. 2 3. 0 16. 0 5. 9 20 30 9. 8 2. 0 2. 8 8. 3 3. 8 3. 3 7. 2 5. 8 3. 7 6. 2 8. 0 4. 2 5. 8 10. 0 4. 6 5. 2 12. 1 5. 0 4. 7 15. 8 5. 5 4. 4 18. 0 6. 0 4. 1 19. 8 6. 3 30 40 12. 0 2. 0 3. 0 10. 3 3. 9 3. 6 8. 9 6. 2 4. 1 7. 8 9. 0 4. 6 7. 1 11. 2 4. 9 6. 5 14. 0 5. 4 5. 8 17. 7 5. 9 5. 4 21. 0 6. 3 5. 1 22. 5 6. 7 40 50 14. 0 2. 0 3. 2 12. 4 4. 0 3. 8 11. 0 6. 5 4. 4 9. 1 9. 8 4. 8 8. 4 12. 2 5. 2 7. 7 15. 7 5. 6 6. 9 19. 8 6. 3 6. 4 23. 0 6. 7 6. 1 25. 0 7. 1 50 60 16. 0 2. 0 3. 5 14. 0 4. 0 4. 0 12. 0 6. 8 4. 6 10. 2 10. 3 5. 1 9. 6 13. 2 5. 5 8. 7 17. 0 6. 0 8. 0 21. 0 6. 5 7. 4 25. 0 7. 0 7. 0 27. 5 7. 5 60 70 18. 0 2. 0 3. 7 15. 8 4. 0 4. 1 13. 5 7. 0 4. 8 11. 9 10. 8 5. 4 10. 5 13. 9 5. 7 9. 9 18. 0 6. 4 9. 0 22. 5 6. 8 8. 3 26. 5 7. 3 7. 8 29. 5 7. 7 70 80 20. 0 2. 0 3. 8 17. 0 4. 0 4. 2 15. 0 7. 2 4. 9 13. 0 11. 0 5. 6 12. 0 14. 5 6. 0 11. 0 18. 9 6. 6 10. 0 24. 0 7. 1 9. 3 28. 0 7. 7 8. 6 31. 5 7. 9 80 90 23. 6 2. 0 3. 9 18. 8 4. 0 4. 3 16. 5 7. 3 5. 1 14. 1 11. 2 5. 8 13. 0 15. 0 6. 3 12. 0 20. 0 6. 7 11. 0 25. 0 7. 2 10. 2 30. 0 7. 9 9. 5 34. 0 8. 2 90 100 27. 1 2. 0 4. 0 20. 0 4. 0 4. 4 17. 5 7. 3 5. 3 15. 1 11. 4 6. 0 14. 0 15. 5 6. 5 12. 8 20. 5 6. 9 11. 9 26. 5 7. 6 11. 0 32. 0 8. 1 10. 3 35. 0 8. 5 100 120 31. 1 2. 0 4. 2 22. 4 4. 1 4. 7 20. 0 7. 8 5. 4 17. 0 11. 7 6. 2 15. 9 16. 0 6. 7 14. 5 21. 5 7. 3 13. 1 27. 5 7. 9 12. 3 33. 5 8. 4 11. 5 37. 5 8. 8 120 140 36. 6 2. 0 4. 5 25. 8 4. 2 4. 9 22. 5 7. 9 5. 8 19. 1 11. 9 6. 4 17. 6 16. 2 7. 0 16. 0 22. 0 7. 6 14. 8 29. 0 8. 3 13. 9 35. 5 8. 8 13. 0 40. 0 9. 2 140 160 43. 2 2. 0 4. 9 28. 4 4. 2 5. 2 24. 3 7. 9 6. 0 21. 1 12. 0 6. 6 19. 5 16. 5 7. 3 18. 0 23. 0 8. 0 16. 4 30. 5 8. 7 15. 1 37. 0 9. 1 14. 5 42. 5 9. 6 160 180 50. 0 2. 0 4. 9 30. 9 4. 3 5. 4 27. 0 8. 0 6. 2 23. 1 12. 1 6. 8 21. 3 17. 0 7. 5 19. 9 23. 5 8. 3 18. 0 31. 5 9. 0 16. 5 38. 5 9. 5 16. 0 44. 5 10. 0 180 200 33. 5 4. 3 5. 6 29. 0 8. 0 6. 4 25. 4 12. 2 7. 1 23. 1 17. 5 7. 7 21. 5 23. 5 8. 5 19. 3 32. 5 9. 2 18. 1 40. 0 9. 8 17. 1 46. 0 10. 3 200 220 36. 5 4. 4 5. 8 31. 1 8. 0 6. 6 27. 2 12. 3 7. 2 25. 0 17. 9 8. 0 22. 9 24. 0 8. 8 20. 9 34. 0 9. 6 19. 1 41. 5 10. 1 18. 2 47. 5 10. 6 220 240 39. 2 4. 4 5. 9 33. 1 8. 0 6. 8 29. 0 12. 4 7. 3 26. 8 17. 9 8. 2 24. 4 24. 5 9. 0 22. 0 34. 5 9. 8 20. 5 43. 0 10. 3 19. 5 49. 0 10. 8 240 260 41. 9 4. 4 6. 0 34. 9 8. 0 6. 9 30. 5 12. 6 7. 5 28. 0 18. 0 8. 4 26. 0 25. 0 9. 2 23. 5 34. 5 10. 0 21. 8 44. 0 10. 6 20. 9 50. 5 11. 1 260 280 44. 5 4. 4 6. 2 36. 8 8. 0 7. 0 32. 4 12. 9 7. 8 29. 5 18. 0 8. 5 27. 7 25. 0 9. 4 25. 0 35. 0 10. 2 23. 0 45. 0 10. 9 22. 0 51. 5 11. 3 280 300 47. 0 4. 4 6. 3 38. 5 8. 0 7. 1 34. 1 13. 1 8. 0 31. 5 18. 0 8. 7 29. 0 25. 0 9. 5 26. 3 35. 0 10. 4 24. 3 45. 0 11. 1 23. 2 53. 0 11. 6 300 320 40. 5 8. 0 7. 2 36. 0 13. 3 8. 2 33. 0 18. 0 8. 9 30. 2 25. 0 9. 6 27. 6 35. 5 10. 6 25. 5 45. 5 11. 2 24. 5 54. 0 11. 8 320 340 42. 4 8. 0 7. 3 37. 6 13. 4 8. 3 34. 2 18. 0 9. 0 31. 6 25. 0 9. 8 29. 0 36. 0 10. 8 26. 7 46. 0 11. 4 25. 5 55. 0 12. 0 340 360 44. 2 8. 0 7. 4 38. 8 13. 4 8. 4 35. 7 18. 1 9. 1 33. 0 25. 0 9. 9 30. 0 36. 5 10. 9 27. 7 46. 5 11. 6 26. 6 55. 0 12. 2 360 380 46. 1 8. 0 7. 5 40. 2 13. 5 8. 5 37. 1 18. 2 9. 3 34. 2 25. 5 10. 0 31. 3 37. 0 11. 1 29. 1 47. 0 11. 8 27. 7 55. 5 12. 4 380 400 48. 0 8. 0 7. 7 42. 2 13. 5 8. 6 38. 8 18. 4 9. 5 35. 6 26. 0 10. 2 32. 5 37. 0 11. 2 30. 2 47. 5 12. 0 28. 9 56. 0 12. 6 400 420 50. 0 8. 0 7. 8 43. 5 13. 6 8. 7 40. 0 18. 7 9. 6 36. 9 26. 5 10. 3 33. 7 37. 5 11. 4 31. 5 47. 5 12. 2 29. 6 56. 5 12. 7 420 440 52. 0 8. 0 7. 9 44. 7 13. 7 8. 8 41. 3 18. 8 9. 7 38. 1 27. 0 10. 4 34. 8 37. 5 11. 5 32. 5 48. 0 12. 3 30. 9 57. 0 12. 9 440 460 54. 0 8. 0 8. 0 46. 2 13. 7 8. 9 42. 8 19. 0 9. 8 39. 5 27. 5 10. 6 36. 0 37. 5 11. 7 33. 5 48. 5 12. 5 31. 8 57. 5 13. 1 460 480 56. 0 8. 0 8. 1 47. 8 13. 7 9. 0 44. 0 19. 0 9. 9 41. 0 27. 5 10. 8 37. 0 37. 5 11. 8 34. 5 49. 0 12. 6 32. 7 57. 5 13. 2 480 500 58. 0 8. 0 8. 2 49. 2 13. 8 9. 1 45. 5 19. 1 10. 1 42. 1 27. 5 10. 9 38. 3 38. 0 11. 9 35. 5 49. 0 12. 7 33. 9 58. 0 13. 4 500 550 53. 0 13. 8 9. 3 48. 5 19. 5 10. 3 44. 9 27. 5 11. 1 41. 0 38. 5 12. 2 38. 2 50. 0 13. 0 36. 5 59. 0 13. 7 550 600 56. 3 13. 8 9. 5 51. 8 19. 7 10. 5 47. 7 27. 5 11. 3 43. 6 39. 0 12. 5 40. 3 50. 0 13. 3 38. 7 60. 0 14. 0 600 650 55. 0 19. 8 10. 7 50. 3 27. 5 11. 6 46. 4 39. 5 12. 8 43. 0 50. 0 13. 7 41. 0 60. 0 14. 2 650 700 58. 5 19. 8 11. 0 53. 2 27. 5 11. 8 49. 0 40. 0 13. 1 45. 4 50. 5 14. 0 43. 5 60. 5 14. 5 700 750 56. 2 27. 5 12. 1 51. 0 40. 0 13. 3 48. 0 51. 0 14. 2 45. 8 61. 0 14. 8 750 800 59. 2 27. 5 12. 3 53. 8 40. 0 13. 5 50. 6 51. 5 14. 5 47. 8 61. 5 15. 0 800 850 56. 2 40. 0 13. 8 52. 5 52. 0 14. 6 50. 0 62. 0 15. 2 850 900 58. 2 40. 0 14. 0 54. 6 52. 0 14. 9 52. 0 62. 5 15 . 5 900 950 57. 2 52. 0 15. 1 54. 0 63. 0 15. 7 950 1000 59. 3 52. 0 15. 3 56. 3 63. 0 16. 0 1000 Table 3302. Minimum Time (T) in hours that wind must blow to form waves of H significant height (in feet) and P period (in secconds). Fetch in nautical miles
445WAVES,BREAKERSANDSURFThe speed(S)ofa free wave in deep water is nearly independent of its height or steepness.For swell, itsrelationship in knots to the period (P) in seconds is given bytheformulaS = 3.03P ,The relationshipfor sea is not known.AAAThe theoretical relationship between speed, wavelength,and period is shown inFigure 3302b.As waves continue onbeyond the generating area, the period, wavelength,andAAAspeed remain the same. Because the waves of each periodhavedifferent speeds they tend to sort themselves byperiodsas they move away from the generating area.The longer pe-riod waves move ata greater speed and moveahead.Atgreatenoughdistancesfroma storm areathewaveswill havesortedthemselves intosetsbasedonperiodFigure 3302c.Interference.The upper part of A shows twowavesofequal heightandnearlyequal lengthtravelinginAll waves are attenuated as they propagate but thethe same direction.The lower part of A shows the resultingshortperiodwaves attenuatefaster,so thatfarfroma stormwavepatterm.InBsimilarinformationisshownforshortonly the longer waves remain.waves and long swell.Thetimeneededfora wavesystemtotravel agivendistance isdoublethatwhichwould beindicatedbytheBecause of the existence of manyindependent wavespeed of individual waves. This is because each leadingsystems at the same time, the sea surface acquires a com-wave in succession gradually disappears and transfers itsplex and irregular pattern. Since the longer waves overrunenergytofollowingwave.Theprocessoccurs suchthatthethe shorter ones, the resulting interference adds to the com-wholewavesystem advances at a speed which is just halfplexity of the pattern.The process of interference,that of each individual wave.This process can easily beillustrated inFigure 3302c,is duplicated many times in theseen in thebow wave of a vessel.The speed at which thewave system advances is called group velocitysea, it is the principal reason that successive waves are noteSOSELENGTH (LLFEETFigure3302b.Relationshipbetween speed, length,andperiodofwaves in deep water,basedupon thetheoreticalrelationshipbetweenperiod and length
WAVES, BREAKERS AND SURF 445 The speed (S) of a free wave in deep water is nearly independent of its height or steepness. For swell, its relationship in knots to the period (P) in seconds is given by the formula The relationship for sea is not known. The theoretical relationship between speed, wavelength, and period is shown in Figure 3302b. As waves continue on beyond the generating area, the period, wavelength, and speed remain the same. Because the waves of each period have different speeds they tend to sort themselves by periods as they move away from the generating area. The longer period waves move at a greater speed and move ahead. At great enough distances from a storm area the waves will have sorted themselves into sets based on period. All waves are attenuated as they propagate but the short period waves attenuate faster, so that far from a storm only the longer waves remain. The time needed for a wave system to travel a given distance is double that which would be indicated by the speed of individual waves. This is because each leading wave in succession gradually disappears and transfers its energy to following wave. The process occurs such that the whole wave system advances at a speed which is just half that of each individual wave. This process can easily be seen in the bow wave of a vessel. The speed at which the wave system advances is called group velocity. Because of the existence of many independent wave systems at the same time, the sea surface acquires a complex and irregular pattern. Since the longer waves overrun the shorter ones, the resulting interference adds to the complexity of the pattern. The process of interference, illustrated in Figure 3302c, is duplicated many times in the sea; it is the principal reason that successive waves are not S 3.03P . = Figure 3302c. Interference. The upper part of A shows two waves of equal height and nearly equal length traveling in the same direction. The lower part of A shows the resulting wave pattern. In B similar information is shown for short waves and long swell. Figure 3302b. Relationship between speed, length, and period of waves in deep water, based upon the theoretical relationship between period and length
446WAVES,BREAKERSANDSURFlittle from its original position.If this were not so,a slowof thesameheight.Theirregularityofthe surfacemaybemovingvesselmightexperienceconsiderabledifficultyinfurtheraccentuatedbythepresenceofwavesystemscross-making way against a wave train.In Figure3303 thefor-ing at an angleto each other,producing peak-like rises.ward displacement is greatly exaggerated.In reporting average wave heights, the mariner has atenencytoneglect the lower ones.It has been found that the3304.EffectsOfCurrentsOnWavesreported value is about the average for the highest one-third. This is sometimes called the“significant"waveAfollowing current increases wavelengths and de-height. The approximate relationship between this heightcreases waveheights.An opposing current has the oppositeand others, is asfollows.effect, decreasing the lengthand increasing the height.Thiseffectcanbe dangerous in certain areas ofthe world whereWaveRelative heighta streamcurrentopposes wavesgeneratedby severeweath-er.An example of this effect is off the Coast of South0.64AverageAfrica,wheretheAgulhas currentis oftenopposedbywest-1.00Significanterly storms, creating steep,dangerous seas.A strong1.29Highest10percentopposing current may cause the waves to break,as in the1.87Highestcaseofoverfallsintidalcurrents.Theextentofwavealter-ation is dependent upon the ratio of the still-water wave3303.PathOfWaterParticlesInAWavespeed to the speed ofthe current.Moderate ocean currents running at obliqueanglestoAsshowninFigure3303,aparticleofwateron thesur-wavedirections appear to have littleeffect, but strong tidalcurrentsperpendiculartoasystemof waveshavebeenob-faceof theoceanfollowsa somewhatcircularorbitasaservedto completelydestroythem in a shortperiod oftimewavepasses,butmovesverylittleinthedirectionofmotionof the wave.Thecommon waveproducing thisaction is3305.TheEffectOf IceOnWavescalled an oscillatory wave. As the crest passes, the particlemovesforward,givingthewatertheappearanceofmovingWhen ice crystalsform in seawater,internal friction iswith the wave.As the troughpasses,themotion is intheop-greatly increased.This results in smoothing of the sea sur-posite direction.The radius of the circular orbit decreasesface.Theeffect of pack ice is even more pronounced.Awith depth, approaching zero at a depth equal to about halfvesselfollowinga lead through such icemaybein smooththewavelength.In shallower waterthe orbits becomemorewater even when agale is blowing and heavy seas are beat-elliptical, and in very shallow water thevertical motion dis-ing against the outer edge of thepack.Hail or torrential rainappearsalmostcompletely.is also effective in flattening the sea,even in a high wind.Since the speed is greater at the top of the orbit than atthe bottom, the particle is not at exactly its original point3306.WavesAndShallowWaterfollowing passageofa wave,buthas moved slightly in thewave's direction ofmotion.However,sincethis advance isWhen a wave encounters shallow water.themove-smallinrelationtotheverticaldisplacement,afloatingob-mentof the water is restricted bythe bottom,resulting inject is raised and lowered by passage of a wave,but movedreduced wave speed. In deep water wave speed is a func-tion of period.In shallow water,the wave speed becomesa function of depth.The shallower thewater,the slowerthe wave speed.As the wave speed slows, the period re-mains the same, so the wavelength becomes shorter.Since the energy in the waves remains the same, theshortening of wavelengths results in increased heights.This process is called shoaling.If the wave approachesa shallow area at an angle, each part is slowed succes-sively as the depth decreases. This causes a change indirection of motion, or refraction,thewavetendingtochange direction parallel to the depth curves.The effectis similartotherefraction of lightandotherforms ofra-diantenergyAs each wave slows, the next wave behind it, in deeperwater, tends to catch up. As the wavelength decreases, theFigure3303.Orbital motion and displacement,s,ofaheightgenerallybecomesgreater.The lower part ofawaveparticle on thesurfaceofdeepwaterduringtwowavebeing nearest the bottom, is slowed more than thetop.Thisperiods.may cause the wave tobecome unstable,the faster-moving
446 WAVES, BREAKERS AND SURF of the same height. The irregularity of the surface may be further accentuated by the presence of wave systems crossing at an angle to each other, producing peak-like rises. In reporting average wave heights, the mariner has a tenency to neglect the lower ones. It has been found that the reported value is about the average for the highest onethird. This is sometimes called the “significant” wave height. The approximate relationship between this height and others, is as follows. 3303. Path Of Water Particles In A Wave As shown in Figure 3303, a particle of water on the surface of the ocean follows a somewhat circular orbit as a wave passes, but moves very little in the direction of motion of the wave. The common wave producing this action is called an oscillatory wave. As the crest passes, the particle moves forward, giving the water the appearance of moving with the wave. As the trough passes, the motion is in the opposite direction. The radius of the circular orbit decreases with depth, approaching zero at a depth equal to about half the wavelength. In shallower water the orbits become more elliptical, and in very shallow water the vertical motion disappears almost completely. Since the speed is greater at the top of the orbit than at the bottom, the particle is not at exactly its original point following passage of a wave, but has moved slightly in the wave’s direction of motion. However, since this advance is small in relation to the vertical displacement, a floating object is raised and lowered by passage of a wave, but moved little from its original position. If this were not so, a slow moving vessel might experience considerable difficulty in making way against a wave train. In Figure 3303 the forward displacement is greatly exaggerated. 3304. Effects Of Currents On Waves A following current increases wavelengths and decreases wave heights. An opposing current has the opposite effect, decreasing the length and increasing the height. This effect can be dangerous in certain areas of the world where a stream current opposes waves generated by severe weather. An example of this effect is off the Coast of South Africa, where the Agulhas current is often opposed by westerly storms, creating steep, dangerous seas. A strong opposing current may cause the waves to break, as in the case of overfalls in tidal currents. The extent of wave alteration is dependent upon the ratio of the still-water wave speed to the speed of the current. Moderate ocean currents running at oblique angles to wave directions appear to have little effect, but strong tidal currents perpendicular to a system of waves have been observed to completely destroy them in a short period of time. 3305. The Effect Of Ice On Waves When ice crystals form in seawater, internal friction is greatly increased. This results in smoothing of the sea surface. The effect of pack ice is even more pronounced. A vessel following a lead through such ice may be in smooth water even when a gale is blowing and heavy seas are beating against the outer edge of the pack. Hail or torrential rain is also effective in flattening the sea, even in a high wind. 3306. Waves And Shallow Water When a wave encounters shallow water, the movement of the water is restricted by the bottom, resulting in reduced wave speed. In deep water wave speed is a function of period. In shallow water, the wave speed becomes a function of depth. The shallower the water, the slower the wave speed. As the wave speed slows, the period remains the same, so the wavelength becomes shorter. Since the energy in the waves remains the same, the shortening of wavelengths results in increased heights. This process is called shoaling. If the wave approaches a shallow area at an angle, each part is slowed successively as the depth decreases. This causes a change in direction of motion, or refraction, the wave tending to change direction parallel to the depth curves. The effect is similar to the refraction of light and other forms of radiant energy. As each wave slows, the next wave behind it, in deeper water, tends to catch up. As the wavelength decreases, the height generally becomes greater. The lower part of a wave, being nearest the bottom, is slowed more than the top. This may cause the wave to become unstable, the faster-moving Wave Relative height Average 0.64 Significant 1.00 Highest 10 percent 1.29 Highest 1.87 Figure 3303. Orbital motion and displacement, s, of a particle on the surface of deep water during two wave periods
447WAVESBREAKERSANDSURF1.21.51.01.4LENGTHANDSPEED0.81.30.61.20.41.10.21.0HEIGHT--J0.90.050.100.150.200.250.300.350.400.450.50Figure 3306.Alteration of the characteristics of waves crossing a shoaltopfallingforward orbreaking.Such a wave is calledasured.Apparently,any heat that may begenerated is dissipatedbreaker, and a series of breakers is surf.to the deeper water beyond the surf zone.Swellpassing over a shoalbut not breaking undergoes3308.WaveMeasurementAboard Shipa decrease in wavelength and speed, and an increase inheight, which may be sudden and dramatic, depending onthe steepness of the seafloor's slope.This ground swellWith suitable equipment and adequate training, reli-may cause heavy rolling if it is on thebeam and its periodablemeasurements oftheheight, length,period, and speedis the sameas theperiod ofroll ofa vessel, even thoughtheof waves can bemade.However,themariner'sestimates ofsea may appear relatively calm. It may also cause a rageheight and length often contain relatively large errors.sea, when theswell waves encounter water shoal enough toThere is a tendency to underestimate the heights of lowmakethembreak.Rageseasaredangeroustosmall craft,waves,and overestimate the heights ofhigh ones.There areparticularlyapproachingfrom seaward,as thevessel canbenumerous accounts of waves 75to80feet high, or evenoverwhelmed by enormous breakers in perfectly calmhigher,although waves morethan55feet highare very rare.weather.The swell waves, ofcourse,mayhavebeen gener-Wavelength is usuallyunderestimated.The motions oftheated hundreds of miles away.In the open ocean they arevessel from which measurements are made contribute toalmost unnoticed due to their very long period and wave-such errors.length.Figure3306 illustrates the approximate alterationofHeight. Measurement of wave height is particularlythe characteristics of waves as they cross a shoal.difficult.A microbarograph can beused if the wave islongenough or the vessel small enough to permit the vessel to3307.EnergyOfWavesridefrom cresttotrough.Ifthewaves areapproaching fromdead ahead or dead astern, this requires a wavelength at leastThe potential energy ofa wave is related to the vertical dis-twice the length of the vessel.For most accurate results thetance of each particle from its stll-water position.Thereforeinstrument should beplaced atthe center ofroll andpitch,topotential energy moves with the wave. In contrast, the kineticminimize the effects of these motions.Wave height can of-energy ofa wave is related to the speed of the particles, distribten be estimated with reasonable accuracyby comparing itutedevenlyalongtheentirewave.with freeboard of the vessel. This is less accurate as waveTheamount ofkinetic energy in a wave istremendous.Aheight and vessel motion increase.If a point of observation4-foot, 10-second wave striking a coast expends more thancan be found at which the top of a wave is in line with the35,000horsepowerpermileofbeach.Foreach56milesofhorizon when the observer is in the trough, the wave heightcoast, the energy expended equals the power generated atis equal to height ofeye.However, ifthe vessel isrolling orHoover Dam. An increase in temperature of the water in the rel-pitching, this height at the moment of observation may beatively narrow surfzone in which this energy is expended woulddifficult to determine. The highest wave ever reliably report-seem tobe indicated,but no pronounced increase hasbeen mea-edwas112feetobservedfromtheUSSRamapoin1933
WAVES, BREAKERS AND SURF 447 top falling forward or breaking. Such a wave is called a breaker, and a series of breakers is surf. Swell passing over a shoal but not breaking undergoes a decrease in wavelength and speed, and an increase in height, which may be sudden and dramatic, depending on the steepness of the seafloor’s slope. This ground swell may cause heavy rolling if it is on the beam and its period is the same as the period of roll of a vessel, even though the sea may appear relatively calm. It may also cause a rage sea, when the swell waves encounter water shoal enough to make them break. Rage seas are dangerous to small craft, particularly approaching from seaward, as the vessel can be overwhelmed by enormous breakers in perfectly calm weather. The swell waves, of course, may have been generated hundreds of miles away. In the open ocean they are almost unnoticed due to their very long period and wavelength. Figure 3306 illustrates the approximate alteration of the characteristics of waves as they cross a shoal. 3307. Energy Of Waves The potential energy of a wave is related to the vertical distance of each particle from its still-water position. Therefore potential energy moves with the wave. In contrast, the kinetic energy of a wave is related to the speed of the particles, distributed evenly along the entire wave. The amount of kinetic energy in a wave is tremendous. A 4-foot, 10-second wave striking a coast expends more than 35,000 horsepower per mile of beach. For each 56 miles of coast, the energy expended equals the power generated at Hoover Dam. An increase in temperature of the water in the relatively narrow surf zone in which this energy is expended would seem to be indicated, but no pronounced increase has been measured. Apparently, any heat that may be generated is dissipated to the deeper water beyond the surf zone. 3308. Wave Measurement Aboard Ship With suitable equipment and adequate training, reliable measurements of the height, length, period, and speed of waves can be made. However, the mariner’s estimates of height and length often contain relatively large errors. There is a tendency to underestimate the heights of low waves, and overestimate the heights of high ones. There are numerous accounts of waves 75 to 80 feet high, or even higher, although waves more than 55 feet high are very rare. Wavelength is usually underestimated. The motions of the vessel from which measurements are made contribute to such errors. Height. Measurement of wave height is particularly difficult. A microbarograph can be used if the wave is long enough or the vessel small enough to permit the vessel to ride from crest to trough. If the waves are approaching from dead ahead or dead astern, this requires a wavelength at least twice the length of the vessel. For most accurate results the instrument should be placed at the center of roll and pitch, to minimize the effects of these motions. Wave height can often be estimated with reasonable accuracy by comparing it with freeboard of the vessel. This is less accurate as wave height and vessel motion increase. If a point of observation can be found at which the top of a wave is in line with the horizon when the observer is in the trough, the wave height is equal to height of eye. However, if the vessel is rolling or pitching, this height at the moment of observation may be difficult to determine. The highest wave ever reliably reported was 112 feet observed from the USS Ramapo in 1933. Figure 3306. Alteration of the characteristics of waves crossing a shoal